Question: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$6.00$, and bags of cookies cost $$2.50$, and sales equaled $$39.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6x+2.5y = 39}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${6x + 2.5}{(x+2)}{= 39}$ Simplify and solve for $x$ $ 6x+2.5x + 5 = 39 $ $ 8.5x+5 = 39 $ $ 8.5x = 34 $ $ x = \dfrac{34}{8.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(4)}{ + 2}$ ${y = 6}$ You can also plug ${x = 4}$ into $ {6x+2.5y = 39}$ and get the same answer for $y$ ${6}{(4)}{ + 2.5y = 39}$ ${y = 6}$ $4$ bags of candy and $6$ bags of cookies were sold.